Technical Field
The present application relates to a method for designing a modulated metasurface antenna. More particularly, the present application relates to designing a surface pattern for a modulated metasurface antenna, i.e., to designing a surface pattern for an impedance surface which, if provided on said impedance surface, results in a position-dependent target impedance of said impedance surface, and the impedance surface having the position-dependent target impedance radiates a desired electromagnetic field radiation in reaction to being irradiated by given electromagnetic field radiation. The present application further relates to an impedance surface having a surface pattern designed by the inventive method and to an antenna provided with an impedance surface having a surface pattern designed by the inventive method.
The disclosure in the present application is particularly though not exclusively applicable to designing impedance surfaces for modulated metasurface antennas for telecommunication applications, space transportation, sensors and remote sensing, medical applications, surveillance, etc., and especially for modulated metasurface antennas for low earth orbit (LEO) satellite platforms.
Description of the Related Art
The main goal of conventional antenna design is to shape an electromagnetic guiding and scattering structure so as to obtain a desired radiation pattern over a given bandwidth. The main limitations of the conventional approach are that the guiding and scattering properties of the materials used in the design are generally input parameters of the design procedure. As a result, the range of antenna configurations and performances that are achievable in the context of conventional antenna design is limited.
As an example of a conventional antenna, a smooth-walled circular wave guide horn may be considered. To improve the radiation pattern and to enlarge the bandwidth of the antenna, it is possible to use corrugated walls. This however leads to a much bulkier structure which is also rather complex and expensive to manufacture. At the same time, the control afforded by the corrugated walls is limited by the fact that it is only known in the prior art how to design an axially symmetric structure with radial corrugations and a longitudinal modulation of width an depth, or an axially symmetric structure with axial corrugations and a radial modulation.
The use of artificial modulated surfaces (metasurfaces) allows for a radical departure from the conventional design procedure by providing extensive control of the impedance or scattering characteristics of the surface, however, at the cost of a rather complex design procedure.
In the above example, a metasurface could be used to replace the corrugated walls of the horn. This would result in a much more compact and lighter structure, which is also easier and less expensive to manufacture. Moreover, the possibility of designing the metasurface with both azimuthal and longitudinal variations offers significantly improved control of the horn behavior and performance.
The use of metasurfaces in antennas is known in the prior art for various goals and for various applications as proposed, e.g., in Sievenpiper, D. F. at al., “Two-Dimensional Beam Steering Using an Electrically Tunable Impedance Surface”, IEEE AP, Vol. 51, Iss. 10, 2003, 2713 - 2722, or in Fusco, V.F. et al., “2-D Anisotropic Textured Surfaces: Properties and Advanced Antenna Applications”, invited paper to EuCAP 2007, Edinburgh, UK, November 2007.
However, the above examples of applications of metasurfaces in the prior art are limited to small antennas and do not feature any modulation of the metasurface itself. The main reason for these limitations is a lack of a robust design procedure for the modulation of the metasurface. Evidently, such design procedure would have to provide sub-wavelength control of the metasurface over several (tens or hundreds) square wavelengths of antenna aperture, taking into account tens of thousands of potentially independent parameters defining the detailed layout of the metasurface.
Recent attempts to address this issue are reported, e.g., in Sievenpiper, D. F. at al., “Holographic Artificial Impedance Surfaces for Conformal Antennas”, IEEE APS/URSI Symposium, Washington, D.C., July 2005, in Minatti, G. et al., “Spiral Leaky-Wave Antennas Based on Modulated Surface Impedance”, IEEE Trans. Antennas and Propagation, Vol. 59, No. 12, pp. 4436 4444, December 2011 (Minatti et al. 2011), or in Minatti, G. et al., “A Circularly-Polarized Isoflux Antenna Based on Anisotropic Metasurface”, IEEE Trans. Antennas and Propagation, Vol. 60, No. 11, pp. 4998 5009, November 2012 (Minatti et al. 2012).
In this context, a metasurface can be defined as a scattering surface that is characterized by a modulation of its scattering tensor. Known implementations of such metasurfaces are based on a dielectric slab backed by a metal plate or having a metalized back surface, having either a thickness that varies across the surface or a pattern of printed metallic patches obtained by repetition (tiling) of a basic sub-wavelength cell, with dimensions and/or orientations of the printed metallic patches changing smoothly across the surface. The modulation of the metasurface controls the conversion of an electromagnetic wave launched on the metasurface (surface wave) into a radiating wave (commonly referred to as leaky-wave). Therein, the specific design of the modulation controls the leakage rate, and thus the antenna beam orientation and shape.
According to a further one of such approaches, which is reported in U.S. Pat. No. 7,911,407 B1 to Fong, B. H. L. et al., a tensorial surface impedance is determined by calculating an outer product between a projection of a desired field pattern on the impedance surface and a surface current on the impedance surface generated by a feed. The tensorial surface impedance is then implemented by patterning the impedance surface with metallic patches, each of the patches being characterized by geometric parameters g, gs, as. A table linking the geometric parameters to values of an impedance tensor of the respective metallic patch is experimentally determined beforehand by providing a sample artificial impedance surface comprised of patches having a given set of parameters, and measuring impedance values for wave propagation along different directions of the sample impedance surface. Providing sample impedance surfaces for several sets of geometric parameters and performing the aforementioned measurements results in said table linking the geometric parameters to values of an impedance tensor. By referring to the table, geometric parameters for each metallic patch on the impedance surface are determined on the basis of local surface impedance at the position of the respective patch, in accordance with the calculated tensorial impedance.
Thus, this prior art approach performs the synthesis of fields (field matching) on the impedance surface, resorting to the well-known properties of surface waves on modulated impedance surfaces. One of the main limitations of this approach lies in the fact that the field matching on the impedance surface makes it difficult to control complex radiation pattern cases as well as complex modulation patterns.
In consequence, this prior art approach does not provide direct feedback on options concerning patch design. Thus, if it is desired to use a different patch design, this different patch design has to be implemented by trial and error. As it further turns out, the approach does not offer measures for avoiding undesired discontinuities that occur in the surface currents (mainly in the phase thereof) and thus occur also in the derivative of the tensorial surface impedance. Lastly, the approach has a limited allowance for performing an optimum selection of the geometric parameters of the patches. For instance, several sets of such geometric parameters may result in the same tensorial surface impedance, while the resulting impedance surfaces would differ in other aspects, such as smoothness of the derivative of the wavevector. Accordingly, the approach does not allow for satisfying secondary requirements such as smoothness of the derivative of the wavevector, which could contribute to minimizing modal conversion and thus to improving the behavior of the impedance surface.
All of the above prior art approaches to designing the modulation of a metasurface are limited in that they are particularly adapted to a particular type of surface structure, e.g., a particular type of printed metal patch, to a design of the feed producing the electromagnetic wave launched on the metasurface, and moreover require knowledge of the desired electromagnetic field projected on the metasurface. Modulation patterns that are obtainable by the above prior art approaches are rather limited, and more complex modulation patterns going beyond, e.g., a sine or cosine dependence of the modulation are not feasible. Moreover, as indicated above also the complexity of radiated fields both with regard to spatial variation and polarization is limited.
Summarizing, presently known design procedures for metasurfaces are specific to the particular implementation of the metasurface and moreover offer little flexibility in adapting to different requirements. Since the range of obtainable modulation patterns is limited, in principle also the range of configurations of the antenna beams scattered by the respective metasurfaces is limited to rather simple configurations, especially with regard to polarization and/or angular variation of the antenna beam.